The theft was reportedly carried out by officers with direct access to cargo, who “regularly siphoned truckloads” of the arms while still delivering some to designated drop-offs.

Jordanian officers who were part of the scheme “reaped a windfall” from sales, using the money to buy iPhones, SUVs and other luxury items, according to a joint investigation by the New York Times and al-Jazeera.

The scheme continued for some time and was only stopped a few months ago when the US became aware of reports arms dealers were bragging that they had large stocks of CIA weapons.

After the Americans complained, Jordanian investigators arrested several dozen “low-level” officers involved in the scheme, but later released them.

It was however discovered that some of the arms were used in the shooting of two American contractors by a Jordanian officer last November at a police training base in the capital Amman.

Husam Abdallat, a senior aide to several past Jordanian prime ministers, said he had heard about the scheme from current Jordanian officials. However state officials denied all the allegations.

The State Department did not address the claims directly, but a spokesman said America’s relationship with Jordan remained solid.

Jordan is one of the US and Britain’s closest and most reliable allies in the Middle East. Washington and London are using the country, which neighbours Syria, as a base to arm and train rebels in the fight against both Islamic State and the Syrian government.

With the US so dependent on Amman the revelation is unlikely to cause serious damage.

Both the CIA and Pentagon programmes in Syria have been plagued by problems since their launch in 2013. The classified CIA programme has managed to train several thousand soldiers and had enjoyed some success against Assad’s government until Russian jets joined the war in support of the president and forced them to retreat.

The Pentagon project, which was aimed at combatting Isil, was shut down after it failed to train enough fighters. Many of those they had managed to send out were either captured or killed by Islamist groups.

Khaled al-Hammad, one of the founders of the New Syrian Army – set up by the US to fight Isil – bemoaned its slow progress in an interview with the Telegraph last week.

He said there were currently fewer than 100 troops on the frontline near the Syria-Jordan border, and that they had been pleading with the US to fly in the 300-some trained fighters waiting in southern Turkey.

“There are hundreds waiting to join us in Turkey and hundreds more who want to sign up, but America keeps delaying. It feels to us like they are not serious about the fight at all.”